The act of burning the United States flag is a very controversial act, in order to help understand this question let's begin by difining what a flag is, (Citizens Flag Alliance and other organizations), define the flag as a cultural artifact, and a symbol of freedom, prosperity and enlightement, what the american society stands for, and it should be protected.
The oponents to this point of view argue that "the flag is a piece of cloth bearing a design for display as a signal, standard etc". (Webster Dictionary).
The opponents of burning of of the flag believe that it does not fall under the protection of the First Admendment, in the case of Texas v. Johnson, Chief Justice William Rehnquist stated that"the flag is the symbol of our Nation, a uniqueness that justifies a govermental prohibition against flag burning", the proponents of burning the flag as a method of expression argue that the First Amendtment,not only protects speech but also protects writing ideas as freedom of speech, and that the First Amendment protects communication no matter what its nature or medium.
The U.S. Supreme Court found that burning of the flag as a form of expresion is protected under the U.S. Constitution, and I belive that this form of expresing an idea should be protected under the First Amendment.